Descriptive results for selected important variables
The mean and standard deviation of the profitability of insurance company were 0.117 and 0.08, respectively.
The average value of managerial efficiency was 0.798 with a standard deviation of 1.855. The average value of firm growth is 0.217 and the value of standard deviation for the same variable is 0.114 which shows that there were slightly significant variations among the values of firm growth as measured by the change in total assets over the years across the sample insurance companies.
On average the liquidity ratio is 1.03 and the value of standard deviation is 0.25. The average value of market share is 0.084 and the value of standard deviation for the same variable is 0.0822 which shows that there were no significant variations among the values of market share (Table 1).
Table 1: Summary results between measurable variable and predictor variables
Variable
|
Observations
|
Mean
|
Std. Dev.
|
Min
|
Max
|
ROA
|
60
|
0.117
|
0.08
|
0.002
|
0 .53
|
Age
|
60
|
16.58
|
9.108
|
2
|
41
|
Branch Distribution
|
60
|
25
|
12.904
|
3
|
70
|
Managerial Efficiency
|
60
|
0.798
|
1.855
|
0 .114
|
14.239
|
Firm Growth
|
60
|
0.217
|
0.114
|
0.017
|
0.505
|
Company Size
|
60
|
8.6105
|
0.3535
|
7.687
|
9.45
|
Tangibility
|
60
|
0.175
|
0.134
|
0.028
|
0.68
|
Leverage
|
60
|
2.5105
|
1.140368
|
0.954
|
7.34
|
Liquidity
|
60
|
1.03
|
0.25
|
0.263
|
1.632
|
Market share
|
60
|
0.084
|
0.0822
|
0.01
|
0.367
|
In our case, all of the VIFs are below 10 and all of the tolerances are close to one indicating that there is no problem of multicollinearity in our data (Table 2).
Table 2: Multicollinearity information of predictor variables
Variable
|
VIF
|
1/VIF
|
Market share
|
10.41
|
0.096097
|
Company share
|
8.18
|
0.122261
|
Branch distribution
|
5.24
|
0.190909
|
Age
|
4.17
|
0.239588
|
Leverage
|
2.83
|
0.353100
|
Liquidity
|
2.31
|
0.432482
|
Firm growth
|
2.29
|
0.435971
|
Tangibility
|
1.85
|
0.539545
|
Managerial
|
1.25
|
0.800549
|
Mean VIF
|
4.28
|
|
Bivariate Analysis Results
Based on the results nine of the five explanatory variables considered in this study were found statistically significantly associated with the return of assets (p<0.25). They are age of companies, firm growth, company size, and leverage and market share.
From the outputs in univariable analysis, one can observe that the predictors age of company, Firm Growth, Company Size, Leverage and market share are highly significant in the univariable analysis However, Branch distribution, Managerial efficiency, Liquidity and Tangibility is not a significant factor for the profitability at 25% level of significance (Table 3).
Table 3: Regression Coefficients
Coefficients
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
Sig.
|
B
|
Std. Error
|
Beta
|
t
|
1
|
(Constant)
|
-0.658
|
0.684
|
|
-0.961
|
0.341
|
Age
|
0.005
|
0.002
|
0.602
|
2.467
|
0.017
|
Branch distribution
|
-0.004
|
0.002
|
-0.612
|
-2.238
|
0.03
|
Managerial efficiency
|
-0.009
|
0.006
|
-0.215
|
-1.614
|
0.113
|
Firm growth
|
-0.094
|
0.126
|
-0.134
|
-0.743
|
0.461
|
Company size
|
0.076
|
0.077
|
0.338
|
0.989
|
0.328
|
Tangibility
|
0.019
|
0.097
|
0.032
|
0.198
|
0.844
|
Leverage
|
0.027
|
0.014
|
0.391
|
1.948
|
0.0057
|
Liquidity
|
0.092
|
0.058
|
0.287
|
1.584
|
0.12
|
Market share
|
-0.175
|
0.375
|
-0.18
|
-0.468
|
0.642
|
a. Dependent Variable: ROA
|
|
|
|
|
Multivariable Analysis of Regression Model
Multivariable analysis indicate that age, branch distribution and leverage were significantly affect and managerial efficiency, firm growth, liquidity, market share, tangibility and company size were not significantly affects the profitability of company (Table 4).
Table 4: Multivariable analysis of regression model
Variables
|
Coeff.
|
Std.Error
|
t-value
|
p-value
|
Confidence Interval
|
Age
|
0.0028926
|
0.0010881
|
2.66
|
0.010
|
[0.0007145, 0.0050707]
|
Branch distribution
|
0.0005328
|
0.0008105
|
0.66
|
0.514
|
[ -.0010896 ,0.0021551]
|
Managerial efficiency
|
-0.0056258
|
0.0056095
|
-1.00
|
0.320
|
[-.0168545 ,0.0056029]
|
Firm Growth
|
-0.105677
|
0.0907648
|
-1.16
|
0.249
|
[-0.2873625, 0.0760084]
|
Company Size
|
0.0351333
|
0.0293344
|
1.20
|
0.236
|
[ -0.0235859 ,0.0938524]
|
Tangibility
|
-0.0621576
|
0.078025
|
-0.80
|
0.429
|
[ -0.2183417, 0.0940265]
|
Leverage
|
0.0114974
|
0.0090805
|
1.27
|
0.211
|
[ -.0066791 ,0.0296739]
|
Liquidity
|
0.0264127
|
0.0419521
|
0.63
|
0.531
|
[-0.0575635 ,0.1103889]
|
Market share
|
0.2352307
|
0.1239301
|
1.90
|
0.063
|
[-0.0128422 ,0.4833037]
|
b. Predictors: (Constant), market share, managerial efficient, tangibility, Firm growth, liquidity, leverage, age, branch distribution Company size
The variables which passed the stepwise variable selection procedure as candidate to be included in the model are: Branch distribution, age and liquidity. One can say that the reduction in the total variation in ROA is about 28.8 % when accounting for market share, managerial efficient, tangibility, Firm growth, liquidity, leverage, age, branch distribution and Company size.
Model Adequacy
The coefficient of determination (R2=68.8%) the goodness of the fitted model approximately good model (Table 5).
Table 5: Model Summary
Model
|
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
1
|
|
.688
|
.659
|
.0733
|
Final Regression Model for Significant Variables.
From the final fitted regression model the intercept, age, and branch distribution are -0.658, 0.005 and -0.004 respectively. Therefore, for every unit increase in age of company the profitability (ROA) increased by 0.005 there is also positive relationship between age of company and return on assets. The average profitability of company is decreased by keeping other variables are constant and if the distribution of branch will increases by one unit the profitability of company decreased by 0.004,keeping other predictor variables, if leverage increases by one unit the profitability of company will be increased by 0.027 birr.
The constant coefficient is -0.658 which indicates the value of the dependent variable (profitability of company) when both of the independent variable (age and branch distribution) are zero. The coefficient associated with age is 0.005 that means when the age of company increases by 1, the amount of profitability of company is expected to increase by holding branch distribution and leverage constant.
The coefficient associated with branch distribution is 0.004 that means profitability will decrease by 0.004 birr on average when branch distribution increases by 1 birr keeping the other independent variable (age and leverage) constant. The coefficient associated with leverage is that means profitability will increased by birr on average when leverage increases by 1 birr keeping the other independent variable (age and branch distribution) constant.
The value suggest that a one unit increase in age of insurance company, on average an increase of about 0.57 units in profitability of insurance company. Similarly, one unit increase in branch distribution leads to a decline of about units in profitability. Finally, one unit increase in leverage ratio leads to an increase of about units in profitability and also suggests a positive relationship between profitability and leverage ratio.
Model Diagnosis and checking assumption
Normality of data
Since the appearance of a histogram can be strongly influenced by the choice of intervals for the bars, to confirm these we can also look at a normal probability plot of the residual (Figure 1).
Checking for the Linearity of Continuous predictor in the regression model
The plots of residual confirm that age of a patient have no linear relationship with the profitability of company (Figure 2).